I have used nine different rifles in four different calibers for cowboy action (if I remember correctly). They were all Marlins except for an Uberti '73 I tried for one match. They had different barrel lengths, some had micro-groove, some had Ballard rifling.
They all worked just fine. The rifle I keep coming back to is a Marlin Cowboy in .44 Special/.44 Magnum with 24" barrel. (Also available as Cowboy Competition with 19" or 20" barrel) I like the longer barrel for the extra weight, holds on target better for me, swings smoother like a long barrel shotgun. Pard I shoot with shoots an 18" barrel with the spring cut down so he can squeeze 10 .38 Special rounds in, he likes it because it is quick and handy, easy to stage.
Whatever Marlin you get take the time to tune it up a bit so it runs smoother and to avoid the "Marlin Jam". I am no gunsmith and I have done several Marlins without messing any of them up so it can't be too hard. Information/directions avaliable here:
http://www.marauder.homestead.com/irons.html
You "may" also want to consider a one piece firing pin and spring kit. I bought mine from Longhunter former End of Trail Top Shooter and really helpful pard.
http://www.longhunt.com/action_work/action_work.shtml#m94
I bought the titanium pin, based on assorted comments if/when I buy another it will be tool steel.
Go to shoots, ask questions, enjoy. What you start with will not be what you are shooting two, four or ten years down the road, or maybe not shooting as often, there is always something different to try.